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ONE STEP EQUATIONS AF 1.1 Objective: Students will solve one-step linear equations in one variable by performing inverse operations, identifying necessary steps, using graphic organizers, writing reflective summaries, and scoring an 80% proficiency on exit slip quizzes and online assessments.

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Key Words Equation Variable Inverse operation

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ONE STEP EQUATIONS An equation is like a balance scale because it shows that two quantities are equal. What you do to one side of the equation must also be done to the other side to keep it balanced.

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ONE STEP EQUATIONS To solve one step equations, you need to ask three questions about the equation: What is the variable? What operation is performed on the variable? What is the inverse operation? (The one that will undo what is being done to the variable)

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**ONE STEP EQUATIONS Example 1 Solve x + 4 = 12 x + 4 = 12 - 4 - 4 x = 8**

What is the variable? The variable is x. What operation is being performed on the variable? Addition. What is the inverse operation (the one that will undo what is being done to the variable)? Subtraction. Using the subtraction property of equality, subtract 4 from both sides of the equation. The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal. x + 4 = 12 - 4 - 4 x = 8

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**ONE STEP EQUATIONS Example 2 Solve y - 7 = -13 y - 7 = -13 + 7 + 7 y =**

What is the variable? The variable is y. What operation is being performed on the variable? Subtraction. What is the inverse operation (the one that will undo what is being done to the variable)? Addition. Using the addition property of equality, add 7 to both sides of the equation. The addition property of equality tells us to add the same thing on both sides to keep the equation equal. y - 7 = -13 + 7 + 7 y = -6

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**ONE STEP EQUATIONS Example 3 Solve –6a = 12 –6a = 12 -6 -6 a = -2**

What is the variable? The variable is a. What operation is being performed on the variable? Multiplication. What is the inverse operation (the one that will undo what is being done to the variable)? Division Using the division property of equality, divide both sides of the equation by –6. The division property of equality tells us to divide the same thing on both sides to keep the equation equal. –6a = 12 -6 -6 a = -2

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**ONE STEP EQUATIONS Example 4 Solve = -10 = -10 2 • = -10 • 2 b = -20**

What is the variable? The variable is b. What operation is being performed on the variable? Division. What is the inverse operation (the one that will undo what is being done to the variable)? Multiplication Using the multiplication property of equality, multiply both sides of the equation by 2. The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal. = -10 2 • = -10 • 2 b = -20

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Combining Like Terms 2 = a + 4.7

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Negative variable -x = -15

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**Dividing a Decimal Equation**

X = 2

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**Solving an Equation Using a Reciprocal**

2 3 4 = x

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**Exit Slip! Solve each equation**

1) 3x = ) –4x = 24 2) 4 + x = ) x = -6 3) X = ) x = 7 -3 4) x – 2 = ) 7x = -49 5) x + 11 = ) –7 + x = 13 8 -9

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